Question

determine the polynomial equation whose roots include the given: 1,2,2,+/_ square root of 2

Answer 1

if any polynomial has a root r then it must contain a factor (x-r).
according to your problem the polynomial must contain
\[(x-1)(x-2)(x-2)(x-\sqrt{2})(x-(-\sqrt{2}))\] now you have to multiply it.....